Physics

The condition of linear instability for a converging cylindrical strong shock wave (SW) in an arbitrary viscous medium is obtained in the limit of a large stationary SW radius, when it is possible to consider the same Rankine-Hugoniot jump relations as for the plane SW. This condition of instability is substantially different from the condition of instability for the plane SW because a cylindrical SW does not have chiral symmetry in the direction of the SW velocity (from left to right or vice versa) as in the case of a plane SW. The exponential growth rate of perturbations for the converging cylindrical SW is positive only for nonzero viscosity in the limit of high, but finite, Reynolds numbers as well as for the instability of a plane SW.

Materials with periodic architectures exhibit many beneficial characteristics such as high specific stiffness thanks to the material placement along the stress paths and the nano-scale strength amplification achieved through the use of hierarchical architectures. Recently, the porosity of architectured materials was leveraged to increase the efficiency of compact heat exchangers, and their internal aerodynamics was studied. However, their performance on external aerodynamics applications is generally assumed to be detrimental. Here, we demonstrate that exposing 3D lattice material to the external flow reduced the drag of a circular cylinder when placed at carefully selected angular locations. We tested two configurations with the lattice material installed at the windward and leeward regions. On the one hand, the windward configuration showed a strong Re dependency, with a drag reduction of up to 45% at Re=11E4. On the other hand, the lattice material in the leeward region reduced the drag by 25% with weak Re dependency. Alterations of the lattice material topology had a noticeable effect on the drag reduction in both cases. Adding aerodynamic features to the already proven beneficial structural properties of 3D lattice materials might aid in the development of low-powered automotive, naval, and aerospace vehicles.

Fully resolved simulations are used to quantify the effects of heat transfer in the presence of buoyancy on the drag of a spatially fixed heated spherical particle at low Reynolds numbers ( Re ) in the range 10 −3 ≤Re≤10 in a variable property fluid. The amount of heat addition from the sphere encompasses both, the heating regime where the Boussinesq approximation holds and the regime where it breaks down. The particle is assumed to have a low Biot number which means that the particle is uniformly at the same temperature and has no internal temperature gradients. Scaling buoyancy with inertial and viscous forces yields two related non-dimensional quantities, called Buoyancy Induced Viscous Reynolds Number ( R e BV ) and Buoyancy Induced Inertial Reynolds Number ( R e BI ). For ideal gases, R e BV is analogous to the Grashof number ( Gr ). No assumptions are made on the magnitude of R e BI (or equivalently R e BV ). The effects of the orientation of gravity relative to the free-stream velocity are examined. Large deviations in the value of the drag coefficient are observed when the Froude number ( Fr ) decreases and/or the temperature of the sphere increases. Under appropriate constraints on R e BI and Re , the total drag on a heated sphere in a low Re flow in the presence of buoyancy (mixed convection) is shown to be, within 10% error, the linear superposition of the drag computed in two canonical setups: one being the drag on a steadily moving heated sphere in the absence of buoyancy (forced convection) and the other being natural convection. However, the effect of temperature variation on the drag of a sphere in both, forced and natural convection, is significant.

Fast contact-line motion of a droplet spreading on a solid substrate under the electrowetting effect generates strong capillary waves on the droplet's surface. The capillary waves may be strong enough to induce ejection of a satellite droplet from the primary one. In this study, we show that the size of the satellite droplet and the ejection time are not only dependent on the contact-line velocity, which directly relates to the applied voltage enabling the electrowetting effect, but also affected by the ejection dynamics. We derive a theoretical model of the criteria for droplet ejection and experimentally verify the proposed criteria for wide ranges of viscosity, droplet size and the applied voltage.

The high-speed impact of a droplet onto a flexible substrate is a highly nonlinear process of practical importance which poses formidable modelling challenges in the context of fluid-structure interaction. We present two approaches aimed at investigating the canonical system of a droplet impacting onto a rigid plate supported by a spring and a dashpot: matched asymptotic expansions and direct numerical simulation (DNS). In the former, we derive a generalisation of inviscid Wagner theory to approximate the flow behaviour during the early stages of the impact. In the latter, we perform detailed DNS designed to validate the analytical framework, as well as provide insight into later times beyond the reach of the proposed mathematical model. Drawing from both methods, we observe the strong influence that the mass of the plate, resistance of the dashpot and stiffness of the spring have on the motion of the solid, which undergoes forced damped oscillations. Furthermore, we examine how the plate motion affects the dynamics of the droplet, predominantly through altering its internal hydrodynamic pressure distribution. We build on the interplay between these techniques, demonstrating that a hybrid approach leads to improved model and computational development, as well as result interpretation, across multiple length- and time-scales.

Most of the works on the dispersion of droplets and their COVID-19 (Coronavirus disease) implications address droplets' dynamics in quiescent environments. As most droplets in a common situation are immersed in external flows (such as ambient flows), we consider the effect of canonical flow profiles namely, shear flow, Poiseuille flow, and unsteady shear flow on the transport of spherical droplets of radius ranging from 5 μ m to 100 μ m, which are characteristic lengths in human talking, coughing or sneezing processes. The dynamics we employ satisfies the Maxey-Riley (M-R) equation. An order-of-magnitude estimate allows us to solve the M-R equation to leading order analytically, and to higher order (accounting for the Boussinesq-Basset memory term) numerically. Discarding evaporation, our results to leading order indicate that the maximum travelled distance for small droplets ( 5μm radius) under a shear/Poiseuille external flow with a maximum flow speed of 1m/s may easily reach more than 250 meters, since those droplets remain in the air for around 600 seconds. The maximum travelled distance was also calculated to leading and higher orders, and it is observed that there is a small difference between the leading and higher order results, and that it depends on the strength of the flow. For example, this difference for droplets of radius 5μm in a shear flow, and with a maximum wind speed of 5m/s , is seen to be around 2m . In general, higher order terms are observed to slightly enhance droplets' dispersion and their flying time.

The number of studies related to unmanned air vehicles (UAV), micro air vehicles (MAV), wind turbines, birds and insects which operate at low Reynolds (Re) numbers have rapidly increased, recently. In this thesis, unsteady aerodynamics of low Reynolds number flows (Re=25000, 50000 and 75000) on NACA4412 airfoil shaped wing which is mainly used in wind turbines and micro air vehicles and operates at low Reynolds numbers and has aspect ratio of 1 (AR=1) was investigated by means of numerous experimental analyses at various angles of attack changing from 0° to 45°. Due to the obtained force measurement results, maximum lift coefficients and stall angles were determined as 1.19, 1.21, 1.24 and 39°, 38°, 37° for Re=25000, 50000 and 75000, respectively. Flow visualization with smoke-wire and oil, velocity distribution experiments were conducted at different planes (z/s= +0.4, +0.2, +0.1, 0, -0.1, -0.2) on the wing. Furthermore, the effects of tip vortices on the wing were determined. The tip vortices were observed at the tip of the wing at low angles of attack and developed through the wake region moved on the wing horizontally with increasing angle of attack and effect of these vortices on the wing increased. It was seen that the tip vortices caused to pressure differences in the wake region and moved to the spanwise direction and this situation led to decrease separation bubble, which is occurred at low Re numbers, and increase stall angle. Additionally, flow condition became steadier due to the tip vortices.

Inertial particles advected by a background flow can show complex structures. We consider inertial particles in a 2D Taylor-Green (TG) flow and characterize particle dynamics as a function of the particle's Stokes number using dynamic mode decomposition (DMD) method from particle image velocimetry (PIV) like-data. We observe the formation of caustic structures and analyze them using DMD to (a) determine the Stokes number of the particles, and (b) estimate the particle Stokes number composition. Our analysis in this idealized flow will provide useful insight to analyze inertial particles in more complex or turbulent flows. We propose that the DMD technique can be used to perform a similar analysis on an experimental system.

Trapped beneath the Antarctic ice sheet lie over 400 subglacial lakes, which are considered to be extreme, isolated, yet viable habitats for microbial life. The physical conditions within subglacial lakes are critical to evaluating how and where life may best exist. Here, we propose that Earth's geothermal flux provides efficient stirring of Antarctic subglacial lake water. We demonstrate that most lakes are in a regime of vigorous turbulent vertical convection, enabling suspension of spherical particulates with diameters up to 36 micrometers. Thus, dynamic conditions support efficient mixing of nutrient- and oxygen-enriched meltwater derived from the overlying ice, which is essential for biome support within the water column. We caution that accreted ice analysis cannot always be used as a proxy for water sampling of lakes beneath a thin (<3.166 kilometers) ice cover, because a stable layer isolates the well-mixed bulk water from the ice-water interface where freezing may occur.

Dynamic mode decomposition (DMD) is utilised to identify the intrinsic signals arising from planetary interiors. Focusing on an axisymmetric quasi-geostrophic magnetohydrodynamic (MHD) wave -called torsional Alfvén waves (TW) - we examine the utility of DMD in two types of MHD direct numerical simulations: Boussinesq magnetoconvection and anelastic convection-driven dynamos in rapidly rotating spherical shells, which model the dynamics in Earth's core and in Jupiter, respectively. We demonstrate that DMD is capable of distinguishing internal modes and boundary/interface-related modes from the timeseries of the internal velocity. Those internal modes may be realised as free TW, in terms of eigenvalues and eigenfunctions of their normal mode solutions. Meanwhile it turns out that, in order to account for the details, the global TW eigenvalue problems in spherical shells need to be further addressed.